fuel pump not turning on

The fuel pump on my 86 s10 blazer does not prime itself when I turn the key to the on position. After trying to start it for 10-15 seconds, the fuel pump turns on and the vehicle starts. This started happening shortly after I replaced the starter, fuel pump, cap/rotor, and after doing some stuff in the steering column. After disconnecting the fuel lines at the throttle body, the fuel pump turns on just fine. When I start the vehicle shortly after it has been driven, the fuel still in the throttle body is enough to start it again and turn the pump on.

May be a bad fuel pump relay.